This logical fallacy is a False Dichotomy (also known as a False Dilemma or Black-and-White Fallacy).
This fallacy occurs when an argument incorrectly presents two opposing options as the only possibilities, when in fact a wide range of other options exist.
How it applies to the statement: The statement "Saying we can’t negatively stereotype basically says you can only have positive opinions about this country" creates a false choice between:
Option A: Engaging in negative stereotypes. Option B: Only having positive opinions. This completely ignores the vast and reasonable middle ground, which is legitimate, specific criticism.